Question

(x-2)(x+2)=4-(x+1)(x-1)

Answer 1

   
[tex]\texttt{Aplicam formula: } (a+b)(a-b)=a^2-b^2 \\ \\ (x-2)(x+2)=4-(x+1)(x-1) \\ x^2-2^2 = 4 - (x^2 - 1^2) \\ x^2-4 = 4 - (x^2 - 1) \\ x^2-4 = 4 - x^2 + 1 \\ x^2-4 - 4 + x^2 - 1 \\ 2x^2 -9 =0 \\ 2x^2 = 9 \\ \displaystyle \\ x^2 = \frac{9}{2} \\ \\ x_{12} = \pm \sqrt{\frac{9}{2} }= \pm \frac{3}{\sqrt{2} }=\pm \frac{3\sqrt{2} }{2} \\ \\ x_1 = \boxed{\frac{3\sqrt{2} }{2}} \\ \\ x_2 = \boxed{-\frac{3\sqrt{2} }{2}} [/tex]

Answer 2

x^2-4=4-(x^2-1)
x^2-4=4-x^2+1
x^2-4-4+x^2-1=0
2x^2 -9=0
2x^2=9
x^2=9/2
x= radical din 9/radical din 2
x=3/radical din 2